Acquiring frequency and phase offset estimates using frequency domain analysis

ABSTRACT

Determining a frequency and phase offset estimates include receiving a signal at an offset estimator. The received signal is zero-padded in the time domain to yield a zero-padded signal. A Fourier transform of the zero-padded signal is taken to yield a transformed signal. The maximum power of the transformed signal is established. Frequency and phase offset estimates are generated based on the maximum power of the transformed signal.

GOVERNMENT FUNDING

The U.S. Government may have certain rights in this invention asprovided for by the terms of Grant Nos. MUOS G8238 TCCPM awarded by theU.S. Navy.

TECHNICAL FIELD

This invention relates generally to the field of signal processing andmore specifically to acquiring frequency and phase offset estimatesusing frequency domain analysis.

BACKGROUND

Certain channel coding techniques allow wireless receivers to operate atlower signal-to-noise ratios than before. As a result, estimatingcarrier offsets to track signals is more challenging. Some knowntechniques use a preamble or amble to remove data modulation, thenestimate frequency offsets using phase differentiation with respect toan elapsed time period. These techniques, however, typically increasenoise, which reduces performance at low signal-to-noise ratios. Otherknown techniques rely on the use of lengthy continuous-wave (CW) oralternating sequence (AS) preambles. These techniques, however,typically result in spectral interference and are well known for theirfalse acquisition.

SUMMARY OF THE DISCLOSURE

According to one embodiment of the present invention, determining afrequency and phase offsets estimate includes receiving a signal at anoffset estimator. The received signal is zero-padded in the time domainto yield a zero-padded signal. A Fourier transform of the zero-paddedsignal is taken to yield a transformed signal. The maximum power of thetransformed signal is established. A frequency offset estimate isgenerated based on the maximum power of the transformed signal. Thefrequency offset may be used to estimate a phase offset.

Certain embodiments of the invention may provide one or more technicaladvantages. A technical advantage of one embodiment may be that afrequency offset is estimated using frequency domain analysis. Theembodiment does not require phase differentiation in the time domainanalysis, which may increase noise. Another technical advantage of oneembodiment may be that a short preamble may be used. The embodiment doesnot require lengthy continuos wave (CW) or alternating sequence (AS)preambles, which typically contribute to undesired spectral interferenceand result in false acquisition. Yet another technical advantage of oneembodiment may be that a digital feed-forward (open loop) topology maybe used. The topology may avoid problems associated with feedbackmethods that deteriorate when used in multipath wireless channels.

Certain embodiments of the invention may include none, some, or all ofthe above technical advantages. One or more other technical advantagesmay be readily apparent to one skilled in the art from the figures,descriptions, and claims included herein.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention and itsfeatures and advantages, reference is now made to the followingdescription, taken in conjunction with the accompanying drawings, inwhich:

FIG. 1 is a block diagram illustrating one embodiment of a system foracquiring frequency and phase offsets; and

FIG. 2 is a flowchart illustrating one embodiment of a method foracquiring frequency and phase offsets that may be used with the systemof FIG. 1.

DETAILED DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention and its advantages are bestunderstood by referring to FIGS. 1 and 2 of the drawings, like numeralsbeing used for like and corresponding parts of the various drawings.

FIG. 1 is a block diagram illustrating one embodiment of a system 10 foracquiring frequency and carrier phase offsets. System 10 may acquirefrequency and carrier phase offsets of a modulated signal usingfrequency domain analysis applied to a data-aided technique. System 10may track the signal using a decision-aided technique.

According to the illustrated embodiment, system 10 includes an input 20,one or more pre-processing modules 22, an offset estimator 24, and oneor more error correction modules 26 coupled as shown. According to oneembodiment of operation, input 20 receives a signal communicatingsymbols. Pre-processing modules 22 perform pre-processing operations onthe received signal. Offset estimator 24 estimates a frequency offsetand a carrier phase offset of the signal using frequency domainanalysis. Error correction modules 26 estimate residual error andcorrect the received signal in accordance with the frequency offsetestimate, the phase offset estimate, and the residual error estimate.

According to one embodiment, a signal may be received at a receiverantenna system. A radio frequency-to-intermediate frequency converterand an analog-to-digital converter may convert the signal. Theconverters may then feed a sampled digital signal to input 20.

A signal refers to an electrical quantity, such as a current or voltage,that may be used to convey symbols through a channel. A signal maycomprise, for example, a coded signal. The signal may include packetizedinformation. A packet 27 of the signal may have any suitable format andsize. Data 28 of packet 27 may be preceded by a pseudo-noise (PN) code29 that may be less than approximately 10% of the total packet length.PN code 29 may be known prior at the receiver, then exploited by offsetestimator 24 using multiplier 40.

Pre-processing modules 22 perform pre-processing operations on thereceived signal such as removing channel gain from the signal, removingsample timing from the signal, decimating the signal, other suitablepre-processing operations, or any combination of the preceding.Pre-processing modules 22 of this embodiment include an automatic gaincontroller (AGC) 30, a delay 32, a multiplier 34, and a decimator 36coupled as shown.

Automatic gain controller 30 estimates the channel gain of the receivedsignal. Automatic gain controller 30 may comprise one or more detectorsoperable to maintain a constant amplitude of a signal by reducing orincreasing the gain of the signal in accordance with the strength of thesignal. Delay 32 delays the received signal for a suitable amount oftime such that the signal and the channel gain estimate for the signalarrive at multiplier 34 at substantially the same time. Delay 32 maycomprise a delay circuit, such as a first-in-first-out (FIFO) circuitthat introduces a time delay. Multiplier 34 removes the channel gainfrom the received signal. Decimator 36 reduces the rate of the receivedsignal.

Offset estimator 24 estimates a frequency offset, a carrier phaseoffset, or both a frequency offset and a carrier phase offset of thereceived signal using frequency domain analysis. A frequency offsetrefers to the difference between a transmitter frequency and a referencefrequency, and a phase offset refers to the difference between the phaseof the received signal and a reference phase, where the difference istypically introduced by the channel through which the received signalhas passed. Offset estimator 24 includes a multiplier 40, a transformer42, a frequency offset estimator 44, and a phase offset estimator 46coupled as shown. Multiplier 40 removes the modulation of the receivedsignal using a pseudo random code 48 to yield a signal with a residualtone that corresponds to the actual frequency offset.

Transformer 42 pads a predetermined window of time that is thought toinclude PN code 29 with zeros and then performs a Fourier transform onthe zero-padded signal to yield a frequency transformed signal.Zero-padding refers to adding one or more zero-valued samples to asignal. Any suitable number of zero-valued samples may be added to anysuitable portion of a signal, such as the beginning, middle, or both thebeginning and middle of the signal. A Fourier transform may refer to adiscrete Fourier transform, such as a fast Fourier transform, used forfrequency analysis of discrete signals. Although transformer 42 is shownperforming the zero-padding and the fast Fourier transform, any numberof modules may perform these operations. Frequency offset estimator 44estimates the frequency offset of the transformed signal, and providesthe frequency offset estimate to phase offset estimator 46. Phase offsetestimator 46 estimates the phase offset from the same transformed signaland the frequency offset estimate.

Error correction modules 26 estimate the residual error and correct thereceived signal for the frequency offset, the phase offset, and theresidual error. Error correction modules 26 include a numericallycontrolled oscillator (NCO) 50, a multiplier 54, a data decoder 56, aphase detector 58, a delay 60, and a loop filter 62 coupled as shown.Error correction modules 26 are coupled to a delay 52 as shown.

Delay 52 delays the received signal for suitable amount of time suchthat the received signal and correction information from numericallycontrolled oscillator 50 arrive at multiplier 54 at substantially thesame time. Delay 52 may comprise a delay circuit, such as a FIFO circuitthat introduces a time delay. Multiplier 54 applies the correctioninformation to the received signal to yield a corrected signal. Decoder56 decodes the corrected signal to yield a decoded signal having thesymbols of the received signal. Delay 60 delays the corrected signal bya single symbol period T such that the delayed signal and the decodedsignal arrive at phase detector 58 at substantially the same time. Delay60 may comprise a delay circuit, such as a FIFO circuit that introducesa time delay.

Phase detector 58, along with loop filter 62 and numerically controlledoscillator 50, form a phase-locked loop. Phase detector 58 compares thereceived delayed signal corrected using estimates from offset estimator24 with the decoded symbols estimate residual error. Phase detector 58may comprise a detector for phase modulation and frequency modulation,and may generate an estimate corresponding to the difference in phasebetween the signals. Loop filter 62 determines an error correction fromthe residual error estimate.

Numerically controlled oscillator 50 receives frequency offset estimatesΔ{circumflex over (f)}, determines corrections in accordance with theestimates, and sends correction information to multiplier 54. Forexample, numerically controlled oscillator 50 receives the phase offsetestimate from phase detector 58, determines phase offset correctionsθ_(k) from estimator 24 and residual errors χ_(k) from the loop filter62, and sends correction information to multiplier 54. Numericallycontrolled oscillator 50 may include one or more circuits operable togenerate a digital oscillating signal. As described previously,multiplier 54 applies the correction information to the received signal.

System 10 may be used for wireless receivers that operate at a lowsignal-to-noise ratio. These wireless receivers may use any suitablechannel coding technique, such as Reed-Solomon coding or turbo codingfor constant envelope bandwidth efficient modulations such as continuousphase frequency shift keying (CPFSK).

Alterations or permutations such as modifications, additions, oromissions may be made to system 10 without departing from the scope ofthe invention. System 10 may have more, fewer, or other modules.Moreover, the operations of system 10 may be performed by more, fewer,or other modules. For example, the operations of transformer 42 may beperformed by more than one module. Additionally, operations of system 10may be performed using any suitable logic comprising software, hardware,other logic, or any suitable combination of the preceding. As used inthis document, “each” refers to each member of a set or each member of asubset of a set.

FIG. 2 is a flowchart illustrating one embodiment of a method foracquiring frequency and carrier phase offsets that may be used with thesystem of FIG. 1. Although the method is described as used with system10 of FIG. 1, the method may be performed using any suitable system foracquiring frequency and carrier phase offsets.

The method begins at step 100, where a signal is received. According tothe illustrated embodiment, input 20 receives a signal that has traveledthrough a channel. A packet of the signal may have, for example, apreamble of L=50 symbols and a total coded packet size of L_(tot)=1024symbols with Minimum Shift Keying (MSK) modulations. The preamblesymbols {c_(k)*} may be less than approximately five or ten percent ofthe total packet size.

The signal is pre-processed at step 102. For example, the signal may besampled by a receiver analog-to-digital (A/D) converter sampling at arate of 1/T_(s), which is an integer multiple of the symbol rate 1/T.The sampled signal y_(k)=y(kT) may be given by Equation (1):y _(k) =g _(k) a _(k) e ^(−j(2πΔf(kT) ^(s) ^(+τ)+θ) ^(k) ⁾ +n _(k)  (1)where k represents the sample T_(s) index, a_(k) represents thetransmitted complex data symbol sample, Δf represents the frequencyoffset, g_(k) represents the channel gain magnitude sample, θ_(k)represents the phase shift introduced by the channel, τ represents thesample timing error, and n_(k) represents the complex additive whiteGaussian noise (AWGN).

According to the illustrated embodiment, automatic gain controller 30estimates the channel gain ĝ_(k). Multiplier 34 removes channel gaing_(k) from signal y(kT_(s)) delayed by delay 32. The sample timing mayalso be removed. To reduce computational complexity, decimator 36 maydecimate signal y(kT_(s)) to a single sample per symbol to yield signaly(kT).

The transmitted modulations of the signal are removed at step 104. Thetransmitted modulations for symbol sample a_(k) may be removed bymultiplying signal y_(k) by a locally generated conjugate replica 48 ofpreamble symbols {c_(k)*}, where * indicates a complex conjugate.According to the illustrated embodiment, multiplier 40 receivespseudo-random code a_(k)* 48 and signal y_(k) to yield unmodulatedsignal z_(k). If the sample timing (T_(s)−τ) is accurate, signal z_(k)may be given by Equation (2):z _(k) =y _(k) c _(k) *=c _(k) *a _(k) e ^(j(2πΔfkT+θ) ^(k) ⁾ +n _(k) c_(k)*  (2)

Since c_(k)*a_(k)=1, the baseband signal z_(k) given by Equation (2) mayalso be described by Equation (2′):z _(k) =e ^(j(2πΔfkT+θ) ^(k) ⁾ +n _(k) c _(k)*  (2′)

The signal is filtered at step 108 to pass through the maximum expectedfrequency offset. For example, a linear bandpass filter (BPF) may have abandwidth that is only wide enough to pass through the maximum expectedfrequency offset BW_(BPF)=A{circumflex over (f)}_(max). The filteringmay reduce the probability of false frequency offset detection due tonoise or spurious receiver emissions.

The signal is zero-padded at step 112. According to the illustratedembodiment, transformer 42 zero-pads signal z_(k). Any suitable numberof zero-valued samples may be added to the signal to zero-pad the signalin any suitable manner. According to one embodiment, to generate a fastFourier transform of N samples for L symbols, N-L zero-valued complexsamples may be appended. For example, to generate a fast Fouriertransform of N=1024 samples for L=50 symbols, N-L=974 zero-valuedcomplex samples may be appended.

A fast Fourier transform (FFT) of the signal is taken at step 116.According to the illustrated embodiment, transformer 42 takes a fastFourier transform of signal z_(k). The resulting transformed signal maybe described by Equation (3):

$\begin{matrix}{{Z(K)} = {\sum\limits_{k = 0}^{N - 1}{\left( {{\mathbb{e}}^{j{({{2\;\pi\;\Delta\;{fkT}} + \theta_{k}})}} + {n_{k}c_{k}^{*}}} \right){\mathbb{e}}^{{- j}\; 2\;\pi\frac{k}{N}k}}}} & (3)\end{matrix}$where k represents the frequency bin index, k=f_(s)/N represents the FFTbin resolution, and f_(s) represents the sampling frequency, which inthis case is equal to the symbol rate (1/T). Any suitable number N ofFFT bins may be used, for example, N=1024, where k ranges from k=0 tok=N−1. The N bins may include a single bin with maximum energyk=k_(max), which corresponds to the frequency offset max estimateΔ{circumflex over (f)}. Because a finite number of bins are used, theactual frequency offset Δ{circumflex over (f)} may not coincide with thea bin, but may spread over multiple bins including k=k_(max).

The frequency offset is estimated at step 120. According to theillustrated embodiment, frequency offset estimator 44 determinesfrequency offset estimate Δ{circumflex over (f)} by locating the FFT bincorresponding to the maximum power. Frequency offset estimateΔ{circumflex over (f)} may be given by Equation (4):

$\begin{matrix}{{\Delta\;\hat{f}} = {\max\limits_{\Delta\; f}{{Z(K)}}}} & (4)\end{matrix}$

Using the estimate obtained by Equation (4), the carrier phase offset isestimated at step 124. According to the illustrated embodiment, phaseoffset estimator 46 determines carrier phase offset estimate {circumflexover (θ)}_(k) according to Equation (5):{circumflex over (θ)}_(k)=arg(Z(K _(max)))−2πΔ{circumflex over(f)}T  (5)where arg(x) represents the argument of complex value x computed usingthe arctangent function, K_(max) is the index of the FFT bincorresponding to the maximum power, and k in this case refers back tothe symbol index. The disturbance terms in Equations (4) and (5) may bedetermined by expanding Equation (3) as Equation (3′):

$\begin{matrix}{{Z(K)} = {{\sum\limits_{k = 0}^{N - 1}{\mathbb{e}}^{j{({{2\;\pi\;\Delta\;{fkT}} + \theta_{k} - {2\;\pi\frac{k}{N}k}})}}} + \underset{\underset{disturbance}{︸}}{\sum\limits_{k = 0}^{N - 1}{n_{k}c_{k}^{*}{\mathbb{e}}^{{- j}\; 2\;\pi\frac{k}{N}k}}}}} & \left( 3^{\prime} \right)\end{matrix}$The offset estimates based on Equations (4) and (5) may have fewerdisturbance terms than estimates obtained using conventional data-aidedmethods. Moreover, the zero-padding performed at step 112 may improveoffset estimates by averaging the estimates over a longer interval Nthan the interval used in conventional data-aided methods.

The signal is corrected at step 128. According to the illustratedembodiment, numerically controlled oscillator (NCO) 50 receives offsetestimates from offset estimator 24 and a residual error correction fromloop filter 62. Numerically controlled oscillator 50 sends correctioninformation to multiplier 54 to correct the offsets and residual errorof signal Y_(k) delayed by delay 52 to yield signal y_(k) given byEquation (6):y _(k) =a _(k) e ^(j(δθ) ^(k) ^(sπkδf(T+δτ))) +n _(k)  (6)where n_(k) is the resulting additive white Gaussian noise AWGN, krepresents the symbol index, δτ represents any timing residual error, δfrepresents the frequency offset residual error, and δθ represents thecarrier phase offset residual error. The frequency offset residual errorand the carrier phase offset residual error result from inaccuracies ofoffset estimators 44 and 46. The signal is decoded at step 130.According to the illustrated embodiment, decoder 56 decodes the signalto yield symbols â_(k).

The residual error is estimated from the decoded signal at step 132. Thecarrier recovery parameters based on Equations (4) and (5) may have someresidual errors due to FFT bin resolution. The undesired phase rotationerror e^(j(δθ) ^(k) ^(+2πkδf(T+δτ))) may be removed using decision-aidedtracking methods. If the network timing is accurate, the timing residualerror δτ may be assumed to be negligible, and so only the error offsetterm e^(j(δθ) ^(k) ^(+2πkδfT)) is tracked and removed. According to theillustrated embodiment, phase detector 58 obtains an error e_(θ)(k) bymultiplying the conjugated symbol â_(k)* from decoder 54 and itscorresponding input sample a_(k)e^(j(δθ) ^(k) ^(+2πδfkT))+n_(k) storedin delay 60, and then taking the imaginary part of the result, yieldingerror signal e_(θ)(k) given by Equation (7):e _(θ)(k)=Im{â _(k) *a _(k) e ^(j(δθ) ^(k) ^(2πδfkT)) +n _(k) â_(k)*}  (7)

Assuming that the transmitted symbols are designed such that|â_(k)*∥a_(k)|=1, and ignoring the noise contribution by the termn_(k)â_(k)*, the error signal e_(θ)(k) may approximated using smallangle approximation by Equation (8):e _(θ)(k)=δθ_(k)+2πδfkT  (8)where k is the symbol index.

Loop filter 62 and numerically controlled oscillator 50 operate on errorsignal e_(θ)(k) to form a phase locked loop (PLL) that is used to trackthe final carrier offsets. Loop filter 62 calculates a signal given byEquation (9):x _(k) =x _(k-1) +K _(p) e _(θ)(k)+K _(i) e _(θ)(k−1)  (9)where the constants K_(p) and K_(i) represent the proportional andintegrator loop coefficients, respectively. The error signal describedby Equation (9) is then sent to numerically controlled oscillator 50,which uses the error signal to correct the signal using multiplier 54.

Depending on the desired tracking loop dynamics, the maximum frequencyresidual error δf_(max) in Equation (7) that the loop can cope with isbounded by δf_(max)≦B_(L), where B_(L) is the tracking loop bandwidththat is largely dependent on K_(p) and K_(i) in Equation (9). The valueof δf_(max), may be used to determine the value of N of Equation (4).

If decoding is to continue at step 136, the method returns to step 128to correct the signal. If decoding is not to continue at step 136, themethod terminates.

According to one example, for a packet size of 1,024 Minimum-ShiftKeying symbols, the method may achieve a perfect carrier offsetestimation at E_(s)/N_(o)=−2 dB, where E_(s)/N_(o) represents the ratioof energy per symbol over the noise within one symbol duration, whileusing only 50 Minimum-Shift Keying PN symbols. Such performance may besuitable for receivers that are required to receive turbo codedsatellite signals or land based long-range line-of-sight communicationnetworks requiring at least E_(s)/N_(o)=2 dB for bit-error rate of 10⁻⁵.

Alterations or permutations such as modifications, additions, oromissions may be made to the method without departing from the scope ofthe invention. The method may include more, fewer, or other steps.Additionally, steps may be performed in any suitable order withoutdeparting from the scope of the invention.

Certain embodiments of the invention may provide one or more technicaladvantages. A technical advantage of one embodiment may be that afrequency offset is estimated using frequency domain analysis. Theembodiment does not require phase differentiation time domain analysis,which may increase noise. Another technical advantage of one embodimentmay be that a short preamble may be used. The embodiment does notrequire lengthy continues wave (CW) or alternating sequence (AS)preambles, which typically contribute to undesired spectral interferenceand result in false acquisition. Yet another technical advantage of oneembodiment may be that a digital feed-forward (open loop) topology maybe used. The topology may avoid problems associated with feedbackmethods that deteriorate when used in multipath wireless channels.

While this disclosure has been described in terms of certain embodimentsand generally associated methods, alterations and permutations of theembodiments and methods will be apparent to those skilled in the art.Accordingly, the above description of example embodiments does notdefine or constrain this disclosure. Other changes, substitutions, andalterations are also possible without departing from the spirit andscope of this disclosure, as defined by the following claims.

1. A method for determining a frequency offset estimate, comprising:receiving a signal at an offset estimator, the signal conveying aplurality of symbols in a plurality of packets, a packet having apreamble comprising a plurality of preamble symbols; zero-padding thereceived signal in a time domain of the received signal with a pluralityof zero-valued samples to yield a zero-padded signal, a number of thezero-valued samples calculated from a difference between a number of aplurality of Fourier transform bins and a number of the preamblesymbols; taking a Fourier transform of the zero-padded signal using theFourier transform bins to yield a transformed signal; establishing amaximum power of the transformed signal; generating a frequency offsetestimate based on the maximum power of the transformed signal; receivingthe frequency offset estimate at a numerically controlled oscillator;receiving a phase offset estimate at the numerically controlledoscillator; receiving a residual error correction at the numericallycontrolled oscillator; and adjusting the received signal in accordancewith the frequency offset estimate, the phase offset estimate, and theresidual error correction.
 2. The method of claim 1, wherein generatingthe frequency offset estimate based on the maximum power of thetransformed signal further comprises generating the frequency offsetestimate as being substantially equivalent to the maximum power of thetransformed signal.
 3. The method of claim 1, further comprisingconverting the received signal to a baseband frequency using thepreamble, the preamble comprising less than ten percent of the packet.4. The method of claim 1, wherein establishing the maximum power of thetransformed signal further comprises locating a Fourier transform bincorresponding to the maximum power.
 5. The method of claim 1, furthercomprising determining a phase offset estimate from a fast Fouriertransform bin corresponding to the maximum power.
 6. The method of claim1, further comprising: generating a decoded signal from the receivedsignal; comparing the received signal with the decoded signal; anddetermining a residual error estimate in accordance with the comparison.7. The method of claim 1, further comprising adjusting the receivedsignal in accordance with at least one of the frequency offset estimate,a phase offset estimate, and a residual error estimate.
 8. The method ofclaim 1, further comprising: adjusting the received signal in accordancewith at least one of the frequency offset estimate, a phase offsetestimate, and a residual error estimate to yield a corrected signal; anddecoding the corrected signal to yield the plurality of symbols.
 9. Asystem for determining a frequency offset estimate, comprising: an inputoperable to receive a signal at an offset estimator, the signalconveying a plurality of symbols in a plurality of packets, a packethaving a preamble comprising a plurality of preamble symbols; atransformer coupled to the input and operable to: zero-pad the receivedsignal in a time domain of the received signal with a plurality ofzero-valued samples to yield a zero-padded signal, a number of thezero-valued samples calculated from a difference between a number of aplurality of Fourier transform bins and a number of the preamblesymbols; and take a Fourier transform of the zero-padded signal usingthe Fourier transform bins to yield a transformed signal; and afrequency offset estimator coupled to the transformer and operable to:establish a maximum power of the transformed signal; generate afrequency offset estimate based on the maximum power of the transformedsignal; and a numerically controlled oscillator operable to: receive thefrequency offset estimate; receive a phase offset estimate; receive aresidual error correction; and adjust the received signal in accordancewith the frequency offset estimate, the phase offset estimate, and theresidual error correction.
 10. The system of claim 9, the frequencyoffset estimator further operable to generate the frequency offsetestimate based on the maximum power of the transformed signal bygenerating the frequency offset estimate as being substantiallyequivalent to the maximum power of the transformed signal.
 11. Thesystem of claim 9, further comprising one or more pre-processing modulesoperable to convert the received signal to a baseband frequency usingthe preamble, the preamble comprising less than ten percent of thepacket.
 12. The system of claim 9, the frequency offset estimatorfurther operable to establish the maximum power of the transformedsignal by locating a Fourier transform bin corresponding to the maximumpower.
 13. The system of claim 9, further comprising determining a phaseoffset estimate from a fast Fourier transform bin corresponding to themaximum power.
 14. The system of claim 9, further comprising one or moreerror correction modules operable to: generate a decoded signal from thereceived signal; compare the received signal with the decoded signal;and determine a residual error estimate in accordance with thecomparison.
 15. The system of claim 9, further comprising one or moreerror correction modules operable to adjust the received signal inaccordance with at least one of the frequency offset estimate, a phaseoffset estimate, and a residual error estimate.
 16. The system of claim9, further comprising one or more error correction modules operable to:adjust the received signal in accordance with at least one of thefrequency offset estimate, a phase offset estimate, and a residual errorestimate to yield a corrected signal; and decode the corrected signal toyield the plurality of symbols.
 17. A system for determining a frequencyoffset estimate, comprising: means for receiving a signal at an offsetestimator, the signal conveying a plurality of symbols in a plurality ofpackets, a packet having a preamble comprising a plurality of preamblesymbols; means for zero-padding the received signal in a time domain ofthe received signal with a plurality of zero-valued samples to yield azero-padded signal, a number of the zero-valued samples calculated froma difference between a number of a plurality of Fourier transform binsand a number of the preamble symbols; means for taking a Fouriertransform of the zero-padded signal using the Fourier transform bins toyield a transformed signal; means for establishing a maximum power ofthe transformed signal; and means for generating a frequency offsetestimate based on the maximum power of the transformed signal; means forreceiving the frequency offset estimate at a numerically controlledoscillator; means for receiving a phase offset estimate at thenumerically controlled oscillator; means for receiving a residual errorcorrection at the numerically controlled oscillator; and means foradjusting the received signal in accordance with the frequency offsetestimate, the phase offset estimate and the residual error correction.18. A method for determining a frequency offset estimate, comprising:receiving a signal at an offset estimator, the signal conveying aplurality of symbols in a plurality of packets, a packet having apreamble comprising a plurality of preamble symbols; converting thereceived signal to a baseband frequency using the preamble, the preamblecomprising less than ten percent of the packet size of the packet;zero-padding the received signal in a time domain of the received signalwith a plurality of zero-valued samples to yield a zero-padded signal, anumber of the zero-valued samples calculated from a difference between anumber of a plurality of Fourier transform bins and a number of thepreamble symbols; taking a Fourier transform of the zero-padded signalusing the Fourier transform bins to yield a transformed signal;establishing a maximum power of the transformed signal by locating aFourier transform bin corresponding to the maximum power; generating afrequency offset estimate from the maximum power of the transformedsignal; generating a phase offset estimate from the maximum power of thetransformed signal; generating a decoded signal from the receivedsignal; comparing the received signal with the decoded signal; anddetermining a residual error estimate in accordance with the comparison;receiving the frequency offset estimate at a numerically controlledoscillator; receiving the phase offset estimate at the numericallycontrolled oscillator; receiving the residual error correction at thenumerically controlled oscillator; and adjusting the received signal inaccordance with the frequency offset estimate, the phase offsetestimate, and the residual error correction; and decoding the correctedsignal to yield the plurality of symbols.